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Introduction to Numerical Analysis for Engineering (13.002J) >> Content Detail



Study Materials



Readings

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Assigned readings are sections in the course textbook: Amazon logo Mathews, J. H., and K. D. Fink. Numerical Methods Using MATLAB®. 3rd ed. Upper Saddle River, NJ: Prentice Hall, 1998. ISBN: 9780132700429.


LEC #TOPICSREADINGS
1Introduction

Computer Architecture

Number Representations

Recursion
Sections 1.1-1.2
2Error Propagation

Error Estimation

Condition Numbers
Sections 1.2-1.3
3Linear Systems of Equations: Cramer's Rule

Gaussian Elimination
Section 1.3
4Linear Systems: Gaussian Elimination

Pivoting

LU Factorization

Error Analysis
Sections 3.1-3.2
5Linear Systems: Tri-Diagonal Systems

Special Matrices
Sections 3.3-3.4 and 3.6
6Linear Systems: Iterative Methods

Convergence of Iterative Schemes
Section 3.4
7Roots of Non-linear Equations: Bisection

Newton-Ralphson Iteration
Section 3.7
8Interpolation of Functions by Polynomials

Lagrange Interpolation

Triangular Family
Sections 2.1-2.4
9Numerical Differentiation and Integration

Error Estimates
Sections 4.1-4.4
10Ordinary Differential Equations

Initial Value Problems: Euler and Runge-Kutta Methods
Sections 6.1-6.2 and 7.1-7.3
11Ordinary Differential Equations (cont.)

Boundary Value Problems: Finite Difference Methods
Sections 9.1-9.2 and 9.4-9.5
12Minimization Problems

Least Square Approximation

Optimization

 








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